Could you please explain what are the physical and theoretical differences between dispersion and diffusion in multi-phase reactors, thanks.
diffusion is simply mass transfer dC/dt = K(C-Ceq), Dispersion includes flow and mixing effects and flows. for example a diffusion model is used to calculate where s plume of pollution from a stack will travel to and what the imact will be.
In a multiphase reactor diffusion incudes mixing effects and flow into and out of the reactor while diffusing is just mass transfer
Going strictly by definition, diffusion is manifestation of species transfer purely by random motion of molecules and is a sub-mechanism of of mass transfer process. Diffusion occurs due to concentration (C) gradient (normal to concentration isosurface) which is explained by chemical potential often expressed as partial derivative of Gibbs energy with respect to species concentration (dG/dC). Diffusive transport of species is best described by the Stefan-Maxwell equation which could be further simplified to obtain the well known Fick's law of diffusion. It is possible to compute diffusion coefficient from first principle approach like Leonard-Jones potential however its parameters (minimal distance between two atoms/molecules and corresponding minimal value of energy) still need to be measured experimentally.
Mass transfer involves the convective transport of species (usually in the direction of flow) which comprises both the advective (transport by fluid flow) and diffusive (transport by molecular motion) component. The above equation that Rick mentioned (although not completely correct) is the usual mass transfer equation which should be written as N = k(C-C*) where N is the mass flux (kg/m2/s), k is the mass transfer coefficient (m/s), C is the non-equilibrium concentration (kmol/m3) of species and C* is the equilibrium concentration. Mass transfer coefficient k is often modelled empirically in terms of Sherwood number correlations which involve both Reynolds number (advective component) and Schmidt number (diffusive component). Mass transfer coefficient at interface is related to diffusion coefficient by the expression k = D/h where h is the boundary layer/film thickness wherein all the resistance to mass transfer is assumed to exist.
Dispersion on the other hand is a measure of flow non-ideality. It indicates deviation from plug flow and often correlated to Peclet number (advection/diffusion). When Pe--> 0, the flow is diffusion dominated and deviates significantly from the plug flow behaviour hence has dispersion ~ 0. Conversely, when Pe-->inf, dispersion dominates and flow behaviour closely resembles plug flow. Dispersion could be best visualised as the spread of a species in a control volume which has a residence time distribution. It differs from diffusion by the flow component/turbulence that the latter doesn't have.
Dear Subhasish, thanks a heap for this helpful and informative discussion.
Hi Hamed, thanks a lot for your contribution to this discussion. Your explanation pretty much matches to mine. However, dispersion and/or diffusion is itself a big research area and further study is must be needed.
The dispersion and convection are the macroscopic phenomena while diffusion is a microscopic phenomenon. Molecules can move one to the other by collision a molecule - molecule - then we have to deal with molecular diffusion. In multi-component systems (N>3) there are also so called cross efects eg. dcA/dz not equal to zera while NA=0 . Molecules can also move without collision in diluted gases (Knudsen diffusion) or in narrow pores of the catalyst by collision the particle-porous wall (Knudsen diffusion). Other types of diffusion are known: eg Volmer's diffusion, diffusion in zeolits and membranes (configurational diffusion) etc. In reactors diffusion occurs in the pores of the catalyst (molecular diffusion and Knudsen diffusion), on the grain surface (may occur Volmer diffusion) and in the layers at the phase boundaries (molecular diffusion). The dispersion may only occur in tubular reactors (so called reverse mixing), while convection dominates in bulk phase in tank-type reactors with stirring.
Fick's type equation describes closely the equimolar counter current diffusion and Knudsen diffusion. In practice, however, it is usually used in many cases. Usually in integration form including covection: NA=kc(cA-cAi), i- interface.
Regards,
Dear Md. Shakhaoath Khan,
All friends' answers are appropriate for your question
Good luck
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